Ordinary and strong density continuity of complex analytic functions

In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:²²,G(x,y)=(x,y ³ ), is not density continuous [1]. We will also characterize those analytic functions which are strongly density continuous at the given pointa . From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b andb is either real or imaginary.     

Some remarks on the theorem of Möbius

H.S.M. Coxeter in his book Introduction to Geometry quotes a theorem of Möbius. In the paper two counterexamples are given. A corrected version of the theorem is stated and proved.     

Simple formula for nuclear charge radius

A new formula for the nuclear charge radius is proposed, dependent on the mass numberA and neutron excessN-Z in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts of even-even nuclei much better than other frequently used relations.This work is partly supported by the Polish Committee of Scientific Research under contract No. 203119101     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solutions. IX. The Mixed Tetragonal Distorted Bis(Salicylato)Cobalt(II) Complex in Various Solvents

Mixed cobalt(II) complexes with the monodentate ligands: 2-hydroxybenzoic acid deprotonated (sal^–, the salicylate ion) and water, have been investigated. The combined results of the spectrophotometric and conductance measurements, as well as known the X-ray structure for solids, were used to determine the structure of the studied complexes in solution. The electronic absorption spectra in aqueous acid (0.01M HClO₄), ethylene glycol (glycol), formamide (FM), N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) solutions have been recorded. The d-d electronic spectra have been treated by the crystal-field model (CFM) and angular overlap model (AOM). Low-symmetry splittings of the broad asymmetric bands in the experimental spectra (solutions at room temperature) were found by Gaussian analysis. The effect of the and bonding of the monodentate ligands (with oxygen-donor ligators) on the central metal ion was described in the ligand–field framework. A comparison of the stereochemistry of the complex species in various solutions was made.     

On Calderón-Toeplitz operators

We discuss boundedness and Schatten ideal criteria for a class of Toeplitz style operators based on the Calderón reproducing formula. These operators are a variation on Calderón-Zygmund operators but our results also apply to classical Toeplitz operators acting on the weighted Bergman space of the upper half plane.     

Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers

A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.     

Diastereoselective synthesis of 2-aminoalkyl-3-sulfonyl-1,3-oxazolidines on solid support

Herein we report our investigation on the oxidation of solid-support-bound amino alcohols to their corresponding aldehydes. These aldehydes were converted into diastereomerically pure (>10:1) 2,4-cis-2-aminoalkyl-3-sulfonyl-1,3-oxazolidines using optically pure 1,2-amino alcohols. The relative configuration was determined using the nuclear Overhauser effect (NOE). The synthesized oxazolidines, which were obtained in high purities, represent a new, diverse scaffold for the solid-phase synthesis of libraries directed toward a pharmacological target.     

Modifying the thermosensitivity of copolymers of sodium styrene sulfonate and<Emphasis Type="Italic"> N</Emphasis>-isopropylacrylamide with dodecyltrimethylammonium chloride

The interactions between copolymers of sodium styrene sulfonate (SSS) and N-isopropylacrylamide (NIPAM), anionic polyelectrolytes, and dodecyltrimethylammonium chloride (DTAC), a cationic surfactant, were studied in aqueous solutions of various ionic strengths. The copolymers were found to be thermoresponsive, showing a lower critical solution temperature (LCST). The influence of the polymer composition, the surfactant concentration, and the ionic strength on the LCST was studied. The surfactant was found to interact strongly with the polymer, forming mixed polymer-surfactant micelles. The critical aggregation concentration (cac) of the polymer-surfactant system was found from fluorescence spectroscopy using pyrene as a fluorescent probe. A strong dependence of the anionic polyelectrolyte-cationic surfactant interactions on the structure of the ionic comonomer was observed.